9:52 webassign.net Example 3 Video Example () Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under the curve y = \\ 3x from 0 to 3. Solution This problem can be solved using disks. To use shells we relabel the curve y = \\ 3x as x = shell height = 3 - 3 X = x = 3 y2/3 shell radius = y For rotation about the x-axis we see that a typical shell has radius y, circumference 2xy, and height So the volume is = 2x In this problem the disk method is simpler. Need Help? Read It 2. [-/0.17 Points] DETAILS SCALCET9 6.3.AE.004. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Example 4 Video Example () y = 25x - Find the volume of the solid obtained by rotating the region bounded by 5x2 and y = 0 about the line x = 10. Solution The following figures show the region and a cylindrical shell formed by rotation about the line x = 10. = 25x - 5 x = 10 x 5 15 20 10 - X- It has radius 10 - x, circumference 2x(10 - x), and height . The volume of the given solid is V = 2x ( 10 - x ) ( 25x - 5x 2 ) dx = 2x (5x3 - 75x2 + 250*) dx = 2x